A331616 E.g.f.: exp(1 / (1 - arcsinh(x)) - 1).

1, 1, 3, 12, 61, 380, 2783, 23240, 217817, 2267472, 25924827, 322257408, 4325450325, 62374428480, 961296291447, 15754664717184, 273537984529713, 5016337928401152, 96871316157146163, 1964030207217042432, 41706446669511523821, 925774982414999202816

Offset

0,3

Comments

a(257) is negative. - Vaclav Kotesovec, Jan 26 2020

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..400

Vaclav Kotesovec, Graph - the asymptotic ratio

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * A296675(k) * a(n-k).

a(n) ~ 8*(-4*Pi*cos(Pi*(n - 4/(4 + Pi^2))/2) - (Pi^2 - 4)*sin(Pi*(n - 4/(4 + Pi^2))/2)) * n^(n-1) / ((4 + Pi^2)^2 * exp(n + 1 - 4/(4 + Pi^2))). - Vaclav Kotesovec, Jan 26 2020

Mathematica

nmax = 21; CoefficientList[Series[Exp[1/(1 - ArcSinh[x]) - 1], {x, 0, nmax}], x] Range[0, nmax]!
A296675[0] = 1; A296675[n_] := A296675[n] = Sum[Binomial[n, k] If[OddQ[k], (-1)^Boole[IntegerQ[(k + 1)/4]] ((k - 2)!!)^2, 0] A296675[n - k], {k, 1, n}]; a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] A296675[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 21}]

Prog

(PARI) seq(n)={Vec(serlaplace(exp(1/(1 - asinh(x + O(x*x^n))) - 1)))} \\ Andrew Howroyd, Jan 22 2020

Crossrefs

Cf. A079484, A296435, A296675, A331607, A331608, A331615, A331617, A331618.

Sequence in context: A235802 A317169 A121694 * A158691 A365299 A038171

Adjacent sequences: A331613 A331614 A331615 * A331617 A331618 A331619

Keyword

sign

Author

Ilya Gutkovskiy, Jan 22 2020

Status

approved